You seem to be primarily interested in red eye and cycle times.
The A95 has the second fastest cycle times without flash but produces red eye. DCRP is the only site that does a red eye shot for all their tests: http://www.dcresource.com/reviews/ca...ot_a95-review/
The DX7590 produces no red eye but the cycle times are similar to the C50 for two shots and is then terrible after the two shots: Not a good choice for cycle times: http://www.dcresource.com/reviews/kodak/dx7590-review/
The Fuji has the fastest cycle times and no red eye. Probably your best bet if shutter lag isn't a problem for you: http://www.dcresource.com/reviews/fu..._s5100-review/
I've had my C50 about 3 years now and found shutter lag a big problem shooting toddlers. It is a nice little camera, but it is missing a feature I never knew to look for. My other two digital cameras aren't that much faster than the C50, but they both have a continuous focus mode. With that you can hold the shutter halfway in pre-focus and if the target moves it will update the focus. So when you want the shot it is almost instant. Half of the toddler pictures of my granddaughter are blurred from the C50 because she was in perpetual motion and the one second shutter delay put her somewhere other than where the camera was focused. With my cameras with continuous focus every shot of her is sharp except for the occasional motion blur.
The A95 is poor for shutter lag. The shutter is about as slow as the C50 and it has no continuous focus mode. It is a nice camera but not for toddlers if shutter lag is a problem for you.
The Kodak is odd in that your shutter lag is faster with the continuous focus turned on even if you don't pre-focus. Most cameras are actually a tad slower or the same if you go through the full autofocus with the continuous focus turned on. The Kodak is about as slow as the C50 without continuous focus at full zoom. With continuous focus turned on it has about half of the shutter lag of the C50 – still not blazing fast but not bad. But if you engage the continuous focus and pre-focus the delay is under 1/10 second.
The Fuji also has a continuous focus mode and extremely fast pre-focus shutter lag. Full shutter lag is a little longer with continuous focus engaged, but you don't use it that way. With continuous focus you can always pre-focus – even on a perpetual motion toddler. I guess you are aware you are losing a Mp with the Fuji compared to your C50. If you never printed a shot larger than 8 X 10 from the Oly it probably won't make any difference. You can also use your xD memory card in the Fuji where you will have to buy new memory with the others.
The full autofocus shutter delay on the C50 is about one second for comparison, and the cycle time 2.9 seconds without flash. These are the speeds of the cameras you are interested in:
DX 7590: http://www.imaging-resource.com/PROD...0/DX75DATA.HTM
None of these cameras have a shutter speed advantage over your C50 if you just press the shutter when you want the shot and don't pre-focus. The Kodak is faster at wide angle but as slow as the C50 zoomed. You can engage the continuous focus and the zoom time on the Kodak improves a little. What you really want to do is engage the continuous focus and use the pre-focus on the Fuji or Kodak. Cycle times are poor on the Kodak, so I think that leaves the Fuji as being the only one with no red eye, decent cycle times and continuous focus to get around shutter lag.
If you don't think you want to mess with pre-focus none of these cameras are going to be much better than your C50 for shutter lag. Imaging resource has a speed page like those linked for every review. Find something in your price range with a full autofocus shutter lag of 0.4 seconds or less if you just want to push the button when you take the picture. You would also want a cycle time under 2 seconds. And you might look at DCRP for the red eye test.
Steve's reviews give cycle times with flash, but you have to dig them out of the conclusions pages. Some cameras really drag out the cycle time with flash, so you should probably read through Steve's conclusions for any camera you are interested in. For example, the Fuji can take as long as 8 seconds for cycle time if you take a flash shot at maximum flash range. You usually shoot closer than that and the flash cycle times are reasonable.